+8 Behavior Entertainment put out a new gaming mechanic that 70% of all other gaming developers report that will bring in a new surge of players. If 10 new players take part in the new mechanic, find the probability that five will stick with the new gaming mechanic.
We can solve this problem using the binomial distribution. Let X be the number of new players who stick with the new gaming mechanic, and let p be the probability that a new player sticks with the new gaming mechanic. Since 70% of all other gaming developers report that the new gaming mechanic will bring in a new surge of players, we have:
p = 0.7
We want to find the probability that five new players stick with the new gaming mechanic, so we have:
X ~ Binomial(n = 10, p = 0.7)
P(X = 5) = (10 choose 5) * (0.7)^5 * (1 - 0.7)^(10 - 5)
Using the formula for the binomial coefficient, we can simplify the expression as:
P(X = 5) = (10! / (5! * (10 - 5)!)) * (0.7)^5 * (0.3)^5
Simplifying further, we get:
P(X = 5) = 252 * 0.16807 * 0.00243
P(X = 5) = 0.102
Therefore, the probability that five new players will stick with the new gaming mechanic is approximately 0.102 or 10.2%.
